This M01PTH I see referenced on schematics

First of all, this is a nonstandard and unhelpful way of calling out component values. Don't do this on schematics you draw! (In normal practice, "R220" means "resistor number 220" and the value is shown separately.)

But somebody with experience might be able to figure it what's going on. Let's see how I do...

C180 must mean 18 pF. Those are crystal load capacitors, which are commonly in the 10 pF - 20 pF range.

C105 means 1 uF. These are bypass capacitors and 1 uF is a common value and the datasheet-recommended value.

R220 probably means 22 ohms, from the example circuits in the 32u2 datasheet.

I found this drawing in the datasheet:

Also notice the supply connections. The micro has its own internal regulator, so the Vcc doesn't need to be connected to anything else (except its bypass capacitor.)

None of the components are super critical. 10% tolerance should be fine.

Once again, don't use this as example of how to draw schematics.

(edited to revise 0.1uF guess to 1 uF.)

I'll take a guess though I don't know for sure. The key words here are publication quality and professor. LaTex does a very nice job when used in conjuction with CircuitTikZ. LaTex is very much used for typesetting documents in the university setting.